Grade 9 Area, Surface Area and Volume

Grade 9 measurement: perimeter and area of 2D shapes and circles, surface area and volume of prisms and cylinders, and unit conversions, with examples.

Measurement in Grade 9 covers the perimeter and area of polygons and circles, and the surface area and volume of cubes, rectangular prisms, triangular prisms and cylinders. You also convert between units such as cm² and m², or cm³ and litres.

These questions are practical, such as how much paint covers a wall or how much water fills a tank. Getting the formulas and units right now sets you up for the pyramids, cones and spheres in Grade 10.

Key concepts

  • Area of a rectangle, triangle (½bh), parallelogram and trapezium
  • Circle: circumference = 2πr and area = πr²
  • Volume of a prism or cylinder = area of base × height
  • Surface area as the total area of all faces (using a net)
  • Unit conversions: 1 m² = 10 000 cm², 1 cm³ = 1 ml, 1 000 cm³ = 1 litre

Worked examples

Find the area of a circle with radius 7 cm (use π ≈ 3.14).

A = πr² = 3.14 × 7² = 3.14 × 49 = 153.86 cm². Its circumference is 2πr = 43.96 cm.

Find the volume of a cylinder with radius 2 cm and height 10 cm (use π ≈ 3.14).

V = πr²h = 3.14 × 4 × 10 = 125.6 cm³.

Find the surface area of a rectangular box 5 cm × 4 cm × 3 cm.

There are three pairs of faces: 2(5 × 4) + 2(5 × 3) + 2(4 × 3) = 40 + 30 + 24 = 94 cm².

A tank holds 0.5 m³ of water. How many litres is that?

1 m³ = 1 000 000 cm³ = 1 000 litres, so 0.5 m³ = 500 litres.

Find the area of a trapezium with parallel sides of 6 cm and 10 cm and a height of 4 cm.

Area = ½ × (sum of the parallel sides) × height = ½ × (6 + 10) × 4 = 32 cm².

Common mistakes

  • Using the diameter instead of the radius in πr².
  • Converting area units with 100 instead of 10 000 (m² to cm²).
  • Mixing up surface area (cm²) and volume (cm³).
  • Forgetting the ½ in the area of a triangle.

Exam tips

  • Write the formula, substitute, then calculate: each step can earn a mark.
  • Convert all measurements to the same unit before you start.
  • Always write the unit in the final answer.

Frequently asked questions

What is the difference between perimeter and area?

Perimeter is the distance around the outside of a shape (cm). Area is the space inside it (cm²).

How many cm² are in a m²?

10 000. A square metre is 100 cm by 100 cm, and 100 × 100 = 10 000.

How do I find the volume of a triangular prism?

Find the area of the triangular face (½ × base × height), then multiply by the length of the prism.

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